Related papers: Dynamics-based machine learning of transitions in …

We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional…

Fluid dynamics spans phenomena from the Cheerios effect to cosmic evolution and has been called the 'queen mother' of science. Traditional modelling relies on numerical methods, including finite differences, volumes, and elements, that…

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

We propose a method to construct a reduced order model with machine learning for unsteady flows. The present machine-learned reduced order model (ML-ROM) is constructed by combining a convolutional neural network autoencoder (CNN-AE) and a…

Elastoinertial turbulence (EIT) is a chaotic state that emerges in the flows of dilute polymer solutions. Direct numerical simulation (DNS) of EIT is highly computationally expensive due to the need to resolve the multi-scale nature of the…

A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…

The problem of classifying turbulent environments from partial observation is key for some theoretical and applied fields, from engineering to earth observation and astrophysics, e.g. to precondition searching of optimal control policies in…

Exact coherent states of a linearly stable, plane parallel shear flow confined between stationary stress-free walls and driven by a sinusoidal body force (a flow first introduced by F. Waleffe, Phys. Fluids 9, 883 (1997)) are computed using…

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…

Continuous-time generative models, such as Flow Matching (FM), construct probability paths to transport between one distribution and another through the simulation-free learning of the neural ordinary differential equations (ODEs). During…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

In this paper, we propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs). From a perspective of physical simulation, we redefine the problem of approximating the gradient flow utilizing…

We investigate theoretically the phase transition in three dimensional cubic Ising model utilizing state-of-the-art machine learning algorithms. Supervised machine learning models show high accuracies (~99\%) in phase classification and…

Boundary layer turbulence, particularly the vertical fluxes of momentum, shapes the evolution of winds and currents and plays a critical role in weather, climate, and biogeochemical processes. In this work, a unified, data-driven…

We investigate the geometric structure of learning dynamics in overparameterized transformer models through carefully controlled modular arithmetic tasks. Our primary finding is that despite operating in high-dimensional parameter spaces…

This work determines the inaccuracy of using Reynolds averaged Navier Stokes (RANS) turbulence models in transition to turbulent flow regimes by predicting the model-based discrepancies between RANS and large eddy simulation (LES) models…

Important classes of active matter systems can be modeled using kinetic theories. However, kinetic theories can be high dimensional and challenging to simulate. Reduced-order representations based on tracking only low-order moments of the…

Data-driven modeling for nonlinear fluid flows using sparse convolution-based mapping into a feature space where the dynamics are Markov linear is explored in this article. The underlying principle of low-order models for fluid systems is…

We present an exact dimensional reduction for high-dimensional dynamical systems composed of $N$ identical dynamical units governed by quasi-linear ordinary differential equations (ODEs) of order $M$. In these systems, each unit follows a…

Incorporating computational fluid dynamics in the design process of jets, spacecraft, or gas turbine engines is often challenged by the required computational resources and simulation time, which depend on the chosen physics-based…